The motion of a particle is represented by $\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}-\mathrm{sint}$. Then,

(1) the particle moving along negative x-direction comes to rest periodically and moves forward.

(2) the particle moving along x-direction comes to rest periodically and moves backwards.

(3) the particle moving along positive x-direction comes to rest periodically and moves forward.

(4) the particle moving along x-direction comes to rest periodically and moves either backwards or forwards.

 

 

 

This objective question is based on NCERT Exemplar subjective Question.

The position of an object is given by $\mathrm{x}\left(\mathrm{t}\right) = \mathrm{A}+{\mathrm{Be}}^{-\mathrm{\gamma t}}, \mathrm{where} \mathrm{A}>\mathrm{B} \mathrm{and} \mathrm{\gamma }>0$, then at any time t:

(1) x < 0, v > 0, a > 0

(2) x > 0, v < 0, a > 0

(3) x < 0, v < 0, a < 0

(4) x < 0, v > 0, a > 0

This objective question is based on NCERT Exemplar subjective Question.

An object falling through a fluid is observed to have acceleration given by a = g - bv, where g = gravitational acceleration and b, is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is:

$\left(1\right) \frac{\mathrm{g}}{\mathrm{b}}$
$\left(2\right) \frac{\mathrm{g}}{{\mathrm{b}}^2}$
$\left(3\right) \frac{{\mathrm{g}}^2}{\mathrm{b}}$
$\left(4\right) \sqrt{\frac{\mathrm{g}}{\mathrm{b}}}$

This objective question is based on NCERT Exemplar subjective Question.

A ball is dropped and its displacement versus time graph is as shown. (Displacement x from the ground and all quantities are positive upwards).

The velocity-time graph of the ball is given by:

1. 

2. 

3. 

4. 

This objective question is based on NCERT Exemplar subjective question.

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. The variation of its acceleration with time is:

(Take acceleration in the backward direction as positive)

1. 

2. 

3. 

4. 

This objective question is based on NCERT Exemplar subjective Question.

Refer to the graph in the figure. Match the following.

Graph        Characteristics

         (i) has v > 0 and a < 0 throughout

         (ii) has x > 0 throughout and has a point with v = 0 and a point with a = 0

         (iii) has a point with zero displacement for t > 0

         (iv) has v < 0 and a > 0

$\left(1\right) \left(\mathrm{a}\right)-\left(\mathrm{ii}\right), \left(\mathrm{b}\right)-\left(\mathrm{iii}\right), \left(\mathrm{c}\right)-\left(\mathrm{i}\right), \left(\mathrm{d}\right)-\left(\mathrm{iv}\right)$
$\left(2\right) \left(\mathrm{a}\right)-\left(\mathrm{iv}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iii}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right)$
$\left(3\right) \left(\mathrm{a}\right)-\left(\mathrm{iii}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iv}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right)$
$\left(4\right) \left(\mathrm{a}\right)-\left(\mathrm{i}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iii}\right), \left(\mathrm{d}\right)-\left(\mathrm{iv}\right)$

This objective question is based on NCERT Exemplar subjective Question.

A person sitting on the ground floor of a building notices through the window, of height \(1.5~\text{m}\), a ball dropped from the roof of the building crosses the window in \(0.1~\text{s}\). What is the velocity of the ball when it is at the topmost point of the window? \(\left(g = 10~\text{m/s}^2\right )\)

A car is moving along a straight line, say \(OP\) in the figure. It moves from \(O\) to \(P\) in \(18\) s and returns from \(P\) to \(Q\) in \(6.0\) s. The average velocity and average speed of the car in going from \(O\) to \(P\) and back to \(Q\) respectively are:

1. \(10\) m/s & \(10\) m/s

2. \(20\) m/s & \(30\) m/s 

3. \(20\) m/s & \(20\) m/s

4. \(10\) m/s & \(20\) m/s

The position of an object moving along \(x\)-axis is given by \(x=a+bt^2\), where \(a=8.5\) m, \(b=2.5 \text{ ms}^{-2}\) and \(t\) is measured in seconds. Its average velocity between \(t=2.0\) s and \(t=4.0\) s is:
1. \(10~\text{m/s}\)
2. \(15~\text{m/s}\)
3. \(20~\text{m/s}\)
4. \(25~\text{m/s}\)

Which of the following does not represent the equation of motion for constant acceleration?